What is the general solution for -0.002=sin(2pi*(3)-500pi(0)+x) ?

The general solution for -0.002=sin(2pi*(3)-500pi(0)+x) is x=-0.00200…+2pin-6pi,x=-5pi+2pin+0.00200…

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-0.002=sin(2pi*(3)-500pi(0)+x)

- 0.002 = sin (2 π \cdot (3) - 500 π (0) + x)

x = - 0.00200 \dots + 2 πn - 6 π, x = - 5 π + 2 πn + 0.00200 \dots

Solution steps

- 0.002 = sin (2 π (3) - 500 π (0) + x)

Switch sides

sin (2 π 3 - 500 π 0 + x) = - 0.002

Apply trig inverse properties

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn, 2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn

Solve

2 π 3 - 500 π 0 + x = arcsin (- 0.002) + 2 πn : x = - arcsin (\frac{1}{500}) + 2 πn - 6 π

Solve

2 π 3 - 500 π 0 + x = π + arcsin (0.002) + 2 πn : x = - 5 π + 2 πn + arcsin (0.002)

x = - arcsin (\frac{1}{500}) + 2 πn - 6 π, x = - 5 π + 2 πn + arcsin (0.002)

Show solutions in decimal form

x = - 0.00200 \dots + 2 πn - 6 π, x = - 5 π + 2 πn + 0.00200 \dots

3 tan (2 x - \frac{π}{2}) = 2 sin (\frac{π}{3})

2 tan (x) - 2 = 0, 0 \leq x \leq 2 π

tan (3 5^{\circ}) tan (5 6^{\circ} - x) = 1

42.25 = 0.1681 cos (b)

\frac{tan ( 3 x )}{tan ( 2 x )} = 1

What is the general solution for -0.002=sin(2pi*(3)-500pi(0)+x) ?
The general solution for -0.002=sin(2pi*(3)-500pi(0)+x) is x=-0.00200…+2pin-6pi,x=-5pi+2pin+0.00200…